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Goldenfeld, N.

Publications and source records attributed to Goldenfeld, N..

Role of long-wavelength degrees of freedom in the rod-to-coil transition in polymers

An analytical model is fitted to experimental data to show that rod-to-coil (RTC) transformations in single strand polymers (SSPs) are close to true phase transitions. The RTC are known to occur when the temperature or pH of a solvent in which the SSP is immersed is varied abruptly. Long wavelength degrees of freedom in the SSPs induce long range interactions in the molecule which lead to a first order phase transition. The Landau formalism suggests that a long-range ordered state can appear at a low temperature. A microscopic model of the phonon degrees of freedom identifies the nonzero temperature threshold at which the phase transition will occur. The phenomenology described is similar to a previous model for transitions in double-strand polymers.

Goldenfeld, N.

Pattern selection in dendritic solidification

It is shown that the dynamically selected velocity and tip radius of dendrites in the boundary-layer model of solidification have the special values which permit the existence of steady-state needle-crystal solutions. This result, in conjunction with considerations of stability, provides new insight concerning the validity of the marginal-stability hypothesis.

Ben-Jacob, E.

Boundary-layer model of pattern formation in solidification

A model of pattern formation in crystal growth is proposed, and its analytic properties are investigated. The principal dynamical variables in this model are the curvature of the solidification front and the thickness (or heat content) of a thermal boundary layer, both taken to be functions of position along the interface. This model is mathematically much more tractable than the realistic, fully nonlocal version of the free-boundary problem, and still recaptures many of the features that seem essential for studying dendritic behavior, for example. Preliminary numerical solutions produce snowflakelike patterns similar to those seen in nature.

Ben-Jacob, E.

Dynamics of interfacial pattern formation

A phenomenological model of dendritic solidification incorporating interfacial kinetics, crystalline anisotropy, and a local approximation for the dynamics of the thermal diffusion field is proposed. The preliminary results are in qualitative agreement with natural dendrite-like pattern formation.

Ben-Jacob, E.